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Both techniques have their advantages and disadvantages. With adaptive subtraction,
the primaries are assumed to have minimum energy because the filters
are estimated in a least-squares senses [equation ()].
In addition, adaptive subtraction is sensitive to
modeling errors (Chapter ). The strengths of
adaptive subtraction are the computing cost and its ease of use, where
the filter and patch sizes are only needed. On the contrary, the
pattern-based approach is more costly (three to four times) because
three inversions need to be run: one for estimating the noise filters
**N**, one for estimating the signal filters **S**, and one for estimating the
primaries [equation ()].
The choice of parameters can be also cumbersome because
filter and patch sizes are needed for the two sets of filters
(noise and signal). In addition, a signal model usually estimated with
the Spitz approximation is needed. The
strengths of the pattern-based approach are its robustness to modeling
uncertainties and the fact that it does not assume that the signal
has minimum energy. These two qualities are particularly important
wherever the multiple model is not accurate enough, as it is the case
for the dataset presented in this Chapter.

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Stanford Exploration Project

5/5/2005